Knowledge and Equilibrium in Games

Abstract

This paper describes an approach to noncooperative game theory that aims to capture considerations that exercise the minds of real-world strategists. The most commonly used tool of noncooperative game theory is the Nash equilibrium. This raises the question: Are there assumptions on what the players in a game think—including what they think other players think, and so on—that lead to consideration of Nash equilibrium? The paper provides answers to this, and related, questions. The approach of this paper involves analyzing the decision problem facing each player in a strategic ("interactive") situation. In addition to grounding game theory in considerations that are of the essence in actual strategic situations, the approach has a number of other objectives: 1) to make game theory more immediately accessible to people who are trained in decision theory but who are not "game theorists" and 2) to make game theory easier to teach to students. Finally, the approach suggests new directions for research into the nature of strategic situations.